Methods and apparatus for determining cardiac output

ABSTRACT

The present invention provides methods and apparatus for determining a dynamical property of the systemic or pulmonary arterial tree using long time scale information, i.e., information obtained from measurements over time scales greater than a single cardiac cycle. In one aspect, the invention provides a method and apparatus for monitoring cardiac output (CO) from a single blood pressure signal measurement obtained at any site in the systemic or pulmonary arterial tree or from any related measurement including, for example, fingertip photoplethysmography. 
     According to the method the time constant of the arterial tree, defined to be the product of the total peripheral resistance (TPR) and the nearly constant arterial compliance, is determined by analyzing the long time scale variations (greater than a single cardiac cycle) in any of these blood pressure signals. Then, according to Ohm&#39;s law, a value proportional to CO may be determined from the ratio of the blood pressure signal to the estimated time constant. The proportional CO values derived from this method may be calibrated to absolute CO, if desired, with a single, absolute measure of CO (e.g., thermodilution). The present invention may be applied to invasive radial arterial blood pressure or pulmonary arterial blood pressure signals which are routinely measured in intensive care units and surgical suites or to noninvasively measured peripheral arterial blood pressure signals or related noninvasively measured signals in order to facilitate the clinical monitoring of CO as well as TPR.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/667,956 filed on Sep. 22, 2003, which claims priority to U.S.Provisional Patent Application 60/446,385, filed Feb. 10, 2003, which ishereby incorporated by reference.

GOVERNMENT SUPPORT

This invention was made with Government Support under Contract/GrantNumbers 6579200 and 6890082 awarded by the National Aeronautics andSpace Administration. The Government has certain rights in theinvention.

BACKGROUND OF THE INVENTION

Cardiac output (CO) is defined to be the volume of blood ejected by theheart per a unit time. Since CO also represents the total flow of bloodsupplying all the tissue beds of the body, it is perhaps the mostindicative quantity of the state of the heart and circulation. CO isroutinely measured in intensive care units and surgical suites in orderto monitor and guide therapy for critically ill patients. These patientsinclude, for example, those in shock (e.g., cardiogenic, hemorrhagic, orseptic) or heart failure and those during and after surgery (e.g.,coronary artery bypass grafting or heart valve replacement.)

An ideal CO measurement technique would be simple to perform,inexpensive, noninvasive or minimally invasive and safe, and veryaccurate. However, none of the conventional measurement techniques knownin the art possess all of these characteristics [10]. For example, thethermodilution technique, which is currently employed in most intensivecare units and surgical suites, involves injecting cold saline into theright atrium and measuring the temperature downstream in the pulmonaryartery. The average CO over the measurement period may than be computedfrom conservation of mass laws. Although the technique is relativelysimple and inexpensive, it requires an invasive right heartcatheterization whose safety is questionable [8, 38] and is not veryaccurate due to the many assumptions upon which it is based (e.g., nosaline recirculation and thorough blood mixing) [10, 27]. The mostaccurate, conventional technique for measuring CO involves surgicallyimplanting a flow probe, either electromagnetic or ultrasonic, directlyon the aorta. Although this technique also provides a continuousmeasurement of CO, it requires a high risk thoracotomy which is rarelyperformed in practice. Moreover, the accuracy of the aortic flow probeis highly dependent on vessel preparation and may only be accurate towithin about 15-20 percent [10, 27].

Although the development of an ideal CO measurement technique has provento be difficult, several ideal, or near ideal, techniques are currentlyavailable for the continuous measurement of peripheral arterial bloodpressure such as Finapres technology [23] and arterial tonometry [25].Previous investigators have therefore sought techniques to monitor COfrom peripheral arterial blood pressure signals. The most populartechniques in the art are the so-called pulse contour methods thatassume the arterial tree to be well represented by a parallelcombination of a capacitor and resistor thereby accounting for thecompliance of the large arteries (AC) and the total peripheralresistance (TPR) of the small arteries. If the instantaneous CO suppliedby the heart is represented as a current source, then the simple modelof the heart and arterial tree in FIG. 1A results. Most of these typesof pulse contour methods are specifically based on mathematical formulaswhich are derived by making simplifying assumptions and approximationsto this model (see, for example, [7, 19-21, 26, 40, 43, 44]). Thesemethods have generally failed to yield good correlation between COdetermined from analysis of ABP signals and directly measured CO over awide range of physiologic conditions [39, 42].

Bourgeois et al. [3, 4] did successfully demonstrate that their pulsecontour method when applied to an ABP signal measured centrally in theaorta could yield a quantity which varied linearly with directlymeasured CO (electromagnetic aortic flow probe) over a wide range ofphysiologic conditions. Their method, which makes no simplifyingassumptions or approximations to the model of FIG. 1A, may be explainedas follows. During the diastolic period of each cardiac cycle, the heartis filling and not supplying blood to the arterial tree (see FIG. 1B).Thus, according to the model, ABP decays with a time constant τ_(D)equal to the product of TPR and AC during each diastolic period (seeFIG. 1B). Since AC is essentially constant over a wide pressure rangeand on the time scale of days [4, 18, 37], CO could then be monitored towithin a constant scale factor (equal to the reciprocal of AC) bydividing the ABP by τ_(D).

Bourgeois et al. specifically demonstrated that beat-to-beat CO may bemonitored from τ_(D) and the governing differential equation of themodel of FIG. 1A. Thus, a key step of the pulse contour method ofBourgeois et al. is to fit an exponential to the diastolic decay portionof an ABP wavelet in order to measure τ_(D). Osbom et al. [34]introduced essentially the same method prior to Bourgeois et al. buttheir experimental validation was not as complete or compelling.

Bourgeois et al. were able to validate their pulse contour method withrespect to a canine ABP signal measured centrally in the aorta, becausethe diastolic portion of such a signal usually resembles an exponentialdecay (see FIG. 2A). These investigators specifically identified theposition in the aorta at the level of the dorsal insertion of thediaphragm as the optimal site for observing an exponential diastolicdecay. However, Bourgeois et al. acknowledged that central ABP is rarelyobtained clinically because of the difficulty in inserting a catheterretrogradely via a peripheral arterial blood vessel and the risk ofblood clot formation and embolization. Moreover, they recognized that,in peripheral ABP signals which are routinely made available inintensive care units and surgical suites usually via a more simple andsafe radial artery catheterization, an exponential diastolic decay isusually not apparent (see FIG. 2B). The method of Bourgeois et al.therefore cannot generally be applied to readily available peripheralABP signals. In fact, its application to central ABP signals may besomewhat limited, as Cundick et al. [9] reported that they could notidentify an optimal location in the human aorta in which the diastolicportion of the ABP signal appeared as a pure exponential decay.

Other pulse contour methods that are based on more complexrepresentations of the arterial tree have also been developed (see, forexample, [5, 11, 12, 16, 24, 31-33, 50]). However, these techniquesrequired the analysis of one, or even two, central ABP signals. Thus,their clinical utility is also severely limited.

Several techniques have more recently been introduced in an attempt tomonitor CO from ABP signals measured peripherally. Techniques based onan adaptive aorta model which require ABP signals measured at twoperipheral sites—the carotid artery and the femoral artery—have beendeveloped [36, 46]. However, catheters are usually not placed forprolonged periods of time at either of these sites in intensive careunits or surgical suites due to issues of safety. Another previoustechnique is based on an empirically-derived formula which involves thecalculation of the derivative of the ABP signal [14]. However, in orderto mitigate the corruptive effects of wave reflections on the derivativecalculation, this technique also requires two peripheral ABPmeasurements, one of which is obtained from the femoral artery. Othertechniques based on a learning approach have been previously proposed[6, 15, 30]. However, these techniques require extremely large sets oftraining data consisting of simultaneous measurements of CO and ABPsignals obtained over the entire range of physiologic conditions.Moreover, the success of these techniques was only demonstrated withcentral ABP signals or only over a narrow physiologic range. Finally,Wesseling et al. [1, 48, 49] and Linton and Linton [28] have recentlyproposed model-based techniques which require only the analysis of asingle radial artery pressure signal. However, Linton and Linton showedthat their technique was reasonably accurate only over a narrow range ofphysiologic conditions, and several previous studies have demonstratedthe inadequacy of the method of Wesseling et al. (see, for example, [13,22]).

It is evident that there remains a need in the art for methods andapparatus for determining CO reliably and accurately using informationobtained from the arterial blood pressure signal. In particular, thereremains a need in the art for methods and apparatus for determining COreliably and accurately using information obtained from the peripheralarterial blood pressure signal.

SUMMARY OF THE INVENTION

The present invention addresses this need, among others. In one aspect,the invention provides for the measuring of a physiologic signalindicative of cardiovascular system activity, e.g., an arterial bloodpressure (ABP) signal over a plurality of cardiac cycles. From analysisof the arterial blood pressure signal or other physiological signal thetimes of the cardiac contractions are identified. Then the relationshipbetween the times of the cardiac contractions and the physiologic signalover a plurality of cardiac cycles is mathematically analyzed. From thisanalysis a mathematical relationship between the occurrence of thecardiac contraction at a certain time and the subsequent time evolutionof the arterial blood pressure over a time period greater than onecardiac cycle is obtained. This mathematical relationship is then usedto determine a dynamical property of the system. For example, in onepreferred embodiment the mathematical relationship is the impulseresponse function between the occurrence of cardiac contractions and thearterial blood pressure signal. In one preferred embodiment thedynamical property is the time constant which describes the decay of theimpulse response function over a time interval, e.g., a time intervalsuch as between 2 and 4 seconds following the maximum height of theexponential. In another preferred embodiment the dynamical property isthe impulse response function itself.

In particular, in a preferred embodiment the invention provides a methodand apparatus for monitoring CO by analyzing the long time scalevariations (greater than a cardiac cycle) in a single ABP signal, whichmay be obtained at any site in the systemic or pulmonary arterial tree.The present invention determines τ_(D) through the analysis of long timeintervals (60-90 second intervals in a preferred embodiment) of an ABPsignal according to the following three steps (see FIG. 3). The firststep involves constructing an impulse train signal, x(t), in which eachimpulse is located at the start of a cardiac contraction and has an areaequal to the ensuing arterial pulse pressure (or an arbitrary constantvalue in another preferred embodiment). The constructed signal thereforeapproximately reflects cardiac contractions in terms of timing andoutput (or just timing, in those embodiments in which the area of theimpulses is an arbitrary constant).

The second step deals with determining the dynamical properties of thearterial tree through the characterization of the relationship betweenthe cardiac contractions and the ABP signal. This is achieved byestimating an impulse response function (h(t)) which when convolved withx(t) best fits the ABP signal (y(t)), according to any of a number ofcriteria. The estimated h(t) represents a normalized ABP response to asingle cardiac contraction. The final step involves fitting anexponential to the tail end of the diastolic decay portion of theestimated h(t) in which the faster wave reflections have vanished inorder to determine τ_(D). Accurate determination of τ_(D) is achieved byvirtue of h(t) coupling the long time scale variations in x(t) to y(t).

The present invention, which in a preferred embodiment includes ananalog-to-digital converter, a buffer system, a signal processing unit,and a display and alarm system (see FIG. 4), may thus be utilized tomonitor CO and/or TPR, to within constant scale factors from anymeasured ABP signal despite the presence of wave reflections. Note thatabsolute CO and/or TPR of the systemic or pulmonary arterial tree(depending on the signal measurement site) may also be determined, ifdesired, by calibration with a single, absolute measure of CO such as athermodilution measurement.

The present invention may be employed in intensive care units andsurgical suites in which invasive radial ABP signals are routinelyavailable and pulmonary ABP signals are sometimes available. The presentinvention may also be applied to noninvasively measured peripheral ABPsignals (e.g., Finapres technology, arterial tonometry) or noninvasivelymeasured signals related to ABP (e.g., fingertip photoplethysmography[45], ear densitography [17]). Thus, the present invention could easilybe employed in primary care settings, emergency rooms, and regularhospital beds in order to facilitate the evaluation of the patient'sheart and circulatory state.

This application refers to various patents and publications. Thecontents of all of these are incorporated by reference.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1A is a simple, lumped model of the heart and arterial tree (eithersystemic or pulmonary). CO is cardiac output; ABP, arterial bloodpressure; TPR, total peripheral resistance; and AC, arterial compliance.

FIG. 1B is a plot of a realistic, continuous CO signal and a plot of theABP signal response to the CO signal determined according to the simplemodel of FIG. 1A. The time constant τ_(D) governs the dynamical behaviorof the simple model.

FIG. 2A is an example of a central ABP signal measured in anexperimental sheep preparation.

FIG. 2B is an example of a peripheral ABP signal measured in thebrachial artery of an experimental dog preparation.

FIG. 3 is an illustration of how one embodiment of the present inventiondetermines τ_(D) from a peripheral ABP signal. PP is arterial pulsepressure; R, the time of the R-wave in a surface electrocardiogram;x(t), an impulse train signal representing cardiac contractions; y(t),an ABP signal; and h(t), the impulse response which when convolved withx(t) best fits y(t).

FIG. 4 is a block diagram of one embodiment of the present invention.

FIG. 5 is the result of a pilot experimental rabbit study whichdemonstrates the correspondence between relative CO changes determinedfrom a femoral ABP signal according to the present invention and anaortic flow probe. CO was altered by various interventions (e.g.,pacing, inferior vena cava balloon occlusion, and nitroglycerine). Thesolid line is the line of identity, and the dashed line is the line thatbest fits the data points.

FIG. 6 shows example excerpts of measured (a) central, (b) “radial”, and(c) femoral arterial blood pressure (ABP) signals from an experimentperformed in swine.

FIG. 7 presents results from animal 1 in an experiment in which themethod of the invention was tested in swine. The top panel illustratesthe aortic flow probe cardiac output (CO) trend (solid), estimated andcalibrated CO trends from the “radial” (dash) and femoral (dash-dot)arterial blood pressure (ABP) signals, and the intervention and duration(underline). The second panel depicts τ_(D) trends estimated from the“radial” (dash) and femoral (dash-dot) ABP signals. The bottom twopanels illustrate the mean ABP (MAP) and heart rate (HR) trends.

FIG. 8 present results from animal 5 in an experiment in which themethod and apparatus of the invention were tested in swine. Panelscorrespond to those in FIG. 7.

DETAILED DESCRIPTION OF CERTAIN PREFERRED EMBODIMENTS OF THE INVENTION

The present invention encompasses the recognition that there issignificant information present in the ABP signal when measured overlong time scales (greater than a single cardiac cycle), and that thisinformation, referred to herein as “long time scale information”, may beused to facilitate determination of dynamical properties of the systemicor pulmonary arterial tree.

Long time scale information incorporates information reflecting thevariability of the ABP signal between beats in addition to, or insteadof, reflecting only information about the ABP signal within singlebeats. Although long time scale information is acquired by measuring theABP signal over a period greater than a single cardiac cycle (typicallyseconds to minutes), not all quantities derived from measurementsperformed over time periods greater than a single cardiac cycle includelong time scale information. For example, it is common to measure ABPover a plurality of cardiac cycles and average the measured amplitudesto obtain mean (average) ABP. However, mean ABP does not incorporatelong time scale information, because it contains no informationreflecting the variability between beats. Once an average value is found(e.g., by integrating the ABP signal over a time interval and dividingby the length of the time interval), information reflecting differencesin length and/or amplitude of the ABP signal is lost. Thus the mean ABPdoes not incorporate long time scale information.

Capturing the information present over long time scales offers a numberof advantages for the determination of dynamical properties of thesystemic or pulmonary arterial tree. In particular, utilizing suchinformation provides a means of accurately determining such propertiesthrough measurement of the ABP signal, despite the fact that the ABPsignal (particularly the peripheral ABP signal) is corrupted by wavereflections that occur at sites of impedance mismatch (e.g., vesselbifurcations).

The inventors have recognized that at sufficiently long time scales, thewavelengths of the propagating waves may be longer than the dimension ofthe arterial tree. Thus the wave reflections corrupt peripheral ABPsignals, but only on relatively short time scales which, however, mayexceed the duration of a single cardiac cycle, leaving the signal onlonger time scales relatively undisturbed. This implies that the lumpedmodel in FIG. 1A is a valid representation of the long time scaledynamics of the arterial tree (either systemic or pulmonary) despite itslimitations as an accurate representation of the arterial tree oversingle cardiac cycles. Moreover, the arterial tree is continuously beingexcited at time scales greater than a cardiac cycle by ongoingperturbations (e.g., breathing) and the dynamic, compensatory responseof the regulatory system (e.g., arterial baroreflex) [2]. Thussignificant long time scale information is generally present in ABPsignals, and the present invention utilizes this information to providemethods for determining dynamical properties of the systemic orpulmonary arterial tree.

The invention provides a method for determining a dynamical property ofthe systemic or arterial tree comprising steps of: (a) measuring aphysiologic signal over a plurality of cardiac cycles; (b) obtaining arelationship between the timing of a cardiac contraction and theevolution of the physiologic signal over a time period greater than thatof a single cardiac contraction cycle by analyzing the physiologicsignal over a plurality of cardiac cycles; and (c) using therelationship to determine the dynamical property. In general, thephysiologic signal is a signal indicative of cardiovascular systemactivity. For example, in certain embodiments of the invention thephysiologic signal is an arterial blood pressure (ABP) signal. Incertain embodiments of the invention the physiologic signal is a signalrelated to the ABP signal. Such related signals include, but are notlimited to, pressure signals obtained using fingertipphotoplethysmography [45], ear densitography [17], etc. In certainembodiments of the invention the physiologic signal is thearterial—systemic filling pressure difference (ASFPD). For purposes ofdescription, the invention will be described in terms of the ABP signal,but it is to be understood that other physiologic signals may besimilarly used.

In general, a dynamical property of a system is a characteristic of thesystem that relates to how the system responds over time to a change inone or more of the parameters of the system. For example, a mathematicalexpression that relates future values of one or more signals generatedby a system to past and present values of signals either sensed orgenerated by the system would constitute a dynamical property of thesystem. A characteristic time is also a dynamical property. In general,a characteristic time indicates the time scale of the temporal evolutionof a function. (For example, for an exponential function given byy(t)=e^(−t/τ), the time constant τ is a characteristic time of thefunction.)

In particular an impulse response function which enables one to computethe expected future values of a signal generated by the system from pastvalues of that signal or past values of other signals either generatedor sensed by the system would constitute a dynamical property of thesystem. The characteristic time of the decay of that impulse responsefunction would also be a dynamical property of the system. Note that thedynamical property need not fully predict how the system responds overtime to a change in one or more of the parameters of the system, ratherit need only be descriptive of the response. Dynamical properties ofsystems can often be estimated from analysis of signals associated withthe system.

The relationship between the timing of a cardiac contraction and theevolution of the ABP signal over time may be obtained in a number ofdifferent ways. Determination of one or more dynamical properties of thesystemic or pulmonary arterial tree in turn allows one to obtain valuesfor a variety of important parameters that characterize thecardiovascular system, including, but not limited to, cardiac output,total peripheral resistance, cardiac index, stroke volume,characteristic time constant, etc.

One application of the methods described above is in measuring cardiacoutput (CO). The invention provides a method of determining cardiacoutput to within a constant scale factor comprising steps of: (a)measuring a physiologic signal over a plurality of cardiac contractioncycles; (b) estimating a function that represents the response of thephysiologic signal to a cardiac contraction over a time period greaterthan that of a single cardiac cycle; (c) determining a characteristictime of the function; (d) determining cardiac output to within aconstant scale factor by dividing the magnitude of the physiologicsignal by the characteristic time obtained in step (c). The inventionfurther provides a method of determining total peripheral resistance towithin a constant scale factor comprising steps of: (a) measuring aphysiologic signal over a plurality of cardiac contraction cycles; (b)estimating a function that represents the response of the physiologicsignal to a cardiac contraction over a time period greater than that ofa single cardiac cycle; and (c) determining a characteristic time of thefunction, wherein total peripheral resistance is given to within aconstant factor by the characteristic time.

In certain embodiments of the invention rather than determining thecharacteristic time of the function estimated in part (b) of the abovemethods, a second function that represents the response of a differentphysiologic signal to a cardiac contraction over a time period greaterthan that of a single cardiac contraction is estimated, and thecharacteristic time of this second function is determined and used instep (d). Accordingly, the invention provides a method of determiningcardiac output to within a constant scale factor comprising steps of:(a) measuring a first physiologic,signal over a plurality of cardiaccontraction cycles; (b) measuring a second physiologic signal over aplurality of cardiac contraction cycles; (c) estimating a function thatrepresents the response of the second physiologic signal to a cardiaccontraction over a time period greater than that of a single cardiaccycle; (d) determining a characteristic time of the function; and (e)determining cardiac output to within a constant scale factor by dividingthe magnitude of the first physiologic signal by the characteristic timeobtained in step (d). The methods will now be described in more detail.

A feature common to the techniques discussed above for monitoring COfrom continuous ABP is that the signal analysis is considered onlywithin individual cardiac cycles. Because of the presence of wavereflections at these time scales, these techniques are limited in thatthey 1) can only be applied to central ABP signal in which thecumulative effects of the pulse reflections are largely attenuated; 2)necessitate two peripheral ABP signal measurements which are not usuallyobtained clinically; 3) require a large set of training data obtainedover a wide range of physiologic conditions, or 4) are reasonablyaccurate only over a limited physiologic range.

In particular, methods that attempt to determine CO by measuring thetime constant (τ_(D)) of the arterial tree, which could then be used tocompute CO to within a constant scale factor (equal to the reciprocal ofAC) have had only limited success for the following reasons. Inperipheral ABP signals such as those typically available in intensivecare units and surgical suites via a technique such as radial arterycatheterization (and also peripheral ABP signals obtained vianon-invasive techniques such as fingertip photoplethysmography or eardensitography), an exponential decay is not usually apparent (see FIG.2B). This is because, as mentioned above, the arterial tree is not alumped system but actually a distributed system with impedancemismatches throughout the system due to vessel tapering and bifurcationsas well as changes in vessel caliber. Thus the diastolic portion (aswell as the systolic portion) of peripheral ABP signals is corrupted bywave reflections that occur at each site of impedance mismatch. (Notethat the complexity of these sites as well as their varying distancesfrom the aorta result in reflected waves with large phasic differenceswhich generally tend to mitigate the cumulative effects of these waveson the central ABP signal.) Even in the case of central APB signals itmay not be possible to identify an optimal location in the human aortaat which the diastolic portion of the ABP signal appears as a pureexponential decay [9]. Similarly, efforts to locate a suitable positionin the pulmonary arterial tree in which the diastolic portions of thepulmonary ABP signal appear as an exponential decay have beenunsuccessful [41].

Thus the presence of wave reflections has impeded development ofaccurate methods to determine the time constant of the arterial tree,which could then be employed to compute CO. As described below, thepresent invention overcomes this difficulty through the use of long timescale information to accurately estimate τ_(D), from which CO may thenbe determined using the following formula:

${CO} = \frac{({ABP})({AC})}{\tau_{D}}$

The scale factor, AC, for a particular individual may be determined byobtaining a single absolute measurement of CO, e.g., by thermodilution,and then solving for AC in the above formula using the estimated valuefor τ_(D). Alternately, AC may be estimated using tables or nomograms,which are well known in the art and may be based on parameters such asage, weight, height, or particular disease status (see, e.g., U.S. Pat.No. 6,485,431). Additional parameters such as total peripheralresistance (TPR), cardiac index, stroke volume (SV), etc., may also bedetermined using well known relationships. For example, TPR=(τ_(D))/AC,TPR=ABP/CO, and SV=(CO)/heart rate.

The CO signal estimated from the formula given above will reflect trueCO over time periods greater than or equal to a single cardiac cycle,but will generately not accurately reflect the cardiac flow signalwithin a single cardiac cycle. For this reason, it may be desirable toaverage the ABP signal or the estimated CO signal over each cardiaccycle. Alternatively, in certain embodiments of the invention the ABPsignal or estimated CO signal is filtered using a low-pass filter with acharacteristic response time greater than the duration of a typicalcardiac cycle. Another alternative is to simply average the ABP signalor estimated CO signal over a time period longer than the duration of atypical cardiac cycle (multibeat averaging). In general, a single-beataverage approach or by use of a low-pass filter with a fairly shortcharacteristic time would be expected to retain the most informationregarding time variation of the CO signal as compared with simpleaveraging of the CO signal over long time periods. The time constantτ_(D) changes slowly in time (because over a time scale of tens ofseconds peripheral resistance is slowly varying and the arterialcompliance AC may be regarded as essentially constant), however thecardiac output itself can vary much more rapidly—on a beat-to-beatbasis. Thus it is generally preferable to estimate the CO from theformula given above together with use of a single beat average orlow-pass filtering approaches—even if the constant τ_(D) is estimatedfrom long epochs of data comprising perhaps tens of seconds—as opposedto simple averaging over time scales long compared to the duration of asingle cardiac cycle.

Although absolute CO may be determined using the formula given above,one important aspect of the invention is the recognition that in manycircumstances it is not necessary to obtain a value for absolute CO. Forexample, in the context of continuous monitoring in the acute setting(e.g., in intensive care units), it is changes in CO rather thanabsolute CO that is most clinically relevant. Thus determination of theproportionality constant is unnecessary, and this potential source oferror may thus be avoided. In other words, the present invention may beused to monitor CO (e.g., identify and quantify changes in CO) insteadof (or in addition to) determining absolute CO.

According to the method of the invention an analog ABP signal ismeasured invasively or noninvasively at any site in the systemic orpulmonary arterial tree. The analog signal is quantized and sampled. Forexample, in a preferred embodiment of the method the signal is quantizedat 12 bits and sampled at 90 Hz. It is noted that these values areexemplary only, and one of ordinary skill in the art will readily beable to select other appropriate values. A signal representing cardiaccontractions is constructed through the formation of an impulse train inwhich each impulse is located at the start of a cardiac contraction andhas an area equal to the ensuing arterial pulse pressure, i.e., thepulse pressure that results from that cardiac contraction (see FIG. 3).The start of each cardiac contraction is determined by detecting theonset of the upstroke of each ABP wavelet, which may be done by any of avariety of methods known in the art, e.g., those described in [51],[52], or [53]. The arterial pulse pressure for each wavelet is given bythe difference in the maximum value of ABP and the value of ABP at theonset of the upstroke.

Alternatively, the area of each impulse may be set to an arbitraryconstant value. In another preferred embodiment, a surfaceelectrocardiogram (ECG) is measured simultaneously with the ABP signal.The two signals are quantized at 12 bits and sampled at 360 Hz. It isnoted that these values are exemplary only, and one of ordinary skill inthe art will readily be able to select other appropriate values. Thestart of each cardiac contraction may then be established by detectingeach R-wave of the ECG. In certain embodiments of the invention theconstructed impulse train and ABP signal are then decimated, e.g., forpurposes of noise reduction. For example, in one embodiment of theinvention the constructed impulse train and ABP signal are decimatedfrom 360 Hz to 90 Hz.

The single contraction ABP response (normalized by approximately theaverage arterial pulse pressure when each impulse is scaled to theensuing arterial pulse pressure), which quantitatively characterizes thedynamical properties of the arterial tree, is determined by estimatingthe discrete-time impulse response function (h(t)) which when convolvedwith the 90 Hz impulse train (x(t)) “best” fits the 90 Hz ABP signal(y(t)) in the least squares sense (see FIG. 3).

The impulse response function is assumed to be well represented by anautoregressive moving average (ARMA) model which is given below:

${{y(t)} = {{\sum\limits_{i = 1}^{m}{a_{i}{y( {t - i} )}}} + {\sum\limits_{i = 1}^{n}{b_{i}{x( {t - i} )}}} + {e(t)}}},$where e(t) is the residual error term, m and n limit the number of termsin the model (model order), and the set of parameters {a_(i), b_(i)}completely defines h(t) [29]. Because the ARMA model is parametric,causality may be imposed, which is necessary for reliably estimatingh(t) as x(t) and y(t) are related in a closed-loop fashion (i.e., y(t)also influences x(t) through the autonomically mediated heart ratebaroreflex) [47].

For a fixed model order, the set of parameters is estimated from 60-90second intervals of x(t) and y(t) through the least-squares minimizationof the residual error term, which has an analytic solution [29]. Themodel order is determined by an ARMA parameter reduction algorithm thatpenalizes for the degree of model complexity [35]. Prior to estimationof h(t), x(t) and y(t) may be lowpass filtered in order to amplify thecontribution of long time scale energy such that the least squares fitbetween x(t) and y(t), at these time scales, is prioritized. Note thatany other parametric model (e.g., autoregressive moving average withexogenous input (ARMAX) model [29]) may be employed in variousembodiments of the invention to represent the structure of h(t), and anyother minimization criterion (e.g., absolute error) may be utilized tofind the “best” h(t). In certain embodiments of the invention the numberof parameters in the model is selected at least in part based on theheart rate.

The τ_(D) quantity is determined by finding the “best” exponential thatfits h(t) over a selected time interval following the time of themaximum value of h(t), preferably a time interval in which the fasterwave reflections have become minimal. For example, as shown in the plotof h(t) presented in FIG. 3, the contribution of the faster wavereflections becomes minimal at approximately 1.5-2 seconds, as evidencedby the decrease in fluctuations of h(t). Following this time the impulseresponse may be accurately approximated as an exponential. Thus incertain preferred embodiments of the invention the selected timeinterval begins approximately 1.5 seconds following the time of maximumh(t), more preferably approximately 2 seconds following the time ofmaximum h(t). For example, it has been found that a time interval of 2to 4 seconds following the time of maximum value of h(t) is suitable.Longer time intervals may also be used. Typically the appropriate timeinterval is predetermined, but in certain embodiments of the inventionit may be selected as the measurements are being made.

The following exponential equation is the basis of the resulting leastsquares problem where A and τ_(D) are parameters to be estimated throughthe least squares minimization of w(t).

${{h(t)} = {{A\;{\mathbb{e}}^{\frac{- l}{\tau_{D}}}} + {w(t)}}},$

By first log transforming h(t) over the interval of interest (which isalways greater than zero), the optimal estimate of the parameters in theleast squares sense may be estimated through an analytic linear leastsquares solution [4]. CO may then be computed to within a constant scalefactor equal to 1/AC through the ratio of the ABP signal to τ_(D) asdiscussed above. Note that TPR of the systemic or pulmonary arterialtree (depending on the signal measurement site) is trivially given, towithin a constant scale factor equal to AC, by τ_(D).

In the embodiment of the invention described above proportional CO isdetermined by dividing ABP by τ_(D). In another embodiment of theinvention, rather than employing ABP, the method uses thearterial—systemic filling pressure difference (ASFPD). The ASFPD isdetermined by subtracting systemic venous pressure from arterial bloodpressure [54]. The systemic filling pressure can either be measured, ormore commonly estimated. All the analyses described above can then beperformed on the ASFPD rather than on the ABP signal, includingestimation of the cardiac output. In this embodiment the ASFPD isdivided by the time constant to obtain a signal proportional to cardiacoutput.

This embodiment of the invention offers a number of potentialadvantages. In the absence of cardiac contractions the arterial bloodpressure would decay over time to the systemic filling pressure, thus itis not fully accurate to describe the decay of the ABP impulse responsefunction at long times as an exponential that decays to zero. However,since in the absence of cardiac contractions the ASFPD does decay tozero, a description in terms of an exponential decay at long times ismore appropriate for the impulse response function of the ASFPD.Furthermore, since the time constant of the impulse response function isestimated at long times when the impulse response function has alreadydecayed substantially, even if the systemic filling pressure is small,there may be a significant difference in the decay constant estimatedfrom the impulse response functions of the ABP compared to theASFPD—with the analysis of the ASFPD providing a more accurate result.

FIG. 4 depicts a block diagram illustrating a preferred embodiment ofthe present invention. An analog ABP signal is fed into ananalog-to-digital converter as it is being measured. The ABP signal maybe acquired using standard methods, such as those mentioned above. Incertain embodiments of the invention a surface electrocardiogram is alsoobtained (ECG), e.g., via standard ECG leads. The digitized ABP signalis stored in a buffer system. The most recent 60-90 second intervals ofthe digitized signal are transferred from the buffer system to aprocessing unit which analyzes the signal according to FIG. 3 in orderto estimate τ_(D). The buffer and processing unit may be implementedusing, for example, any standard microcomputer running appropriatesoftware to implement the mathematical operations described above. Thesoftware components of the invention may be coded in any suitableprogramming language and may be embodied in any of a range ofcomputer-readable media including, but not limited to, floppy disks,hard disks, CDs, zip disks, DVD disks, etc. Outputs such as proportionalCO, CO, and TPR may be displayed on a visual display such as a computerscreen and/or may be printed or transmitted to a remote location. TheECG, and analysis thereof, may also be displayed. In a preferredembodiment of the system the process is continuously repeated therebyproviding the on-line monitoring of CO and TPR (with a delay of 30-45seconds). Finally, in certain embodiments of the invention an alarm istriggered upon excessive decreases in CO.

Alternatively, the AC proportionality constant may be computed with asingle absolute measure of CO (e.g., thermodilution) through the productof τ_(D) and the measured CO divided by ABP, as discussed above. Theproportionality constant AC may then be utilized to obtain absolutemeasures of CO and TPR. Note that physiologic changes in AC due todisease or aging may also be monitored with multiple, simultaneousmeasurements of absolute CO and an ABP signal.

The present invention was evaluated in a pilot study in which femoralABP and aortic flow probe CO were simultaneously measured in anexperimental rabbit preparation during various interventions known toalter CO (e.g., pacing, inferior vena cava balloon occlusion, andnitroglycerine). FIG. 5 illustrates that the resulting relative changesin CO with respect to baseline predicted by the present inventioncorrespond to those changes determined from the aortic flow probe. InFIG. 5 the x-axis represents the percentage change in CO as measuredusing the aortic flow probe, while the y-axis represents the percentagechange in CO as determined using the present invention. The solid line(line of identity) represents results that would be achieved by atechnique that precisely replicated the aortic flow probe measurements.The dashed line represents the values measured using the presentinvention and demonstrates a very close fit.)

The invention was further evaluated in six experiments in swine, inwhich peripheral ABP signals and independent CO via an aortic flow probewere simultaneously measured over a wide physiologic range. SixYorkshire swine (30-34 kg) were studied under a protocol approved by theMIT Committee on Animal Care. The animals were given intramusculartiletamine-zolazepam, xylazine, and atropine prior to endotrachealintubation. The swine were then maintained in a deep plane of anesthesiawith inhaled isoflorane 0.5%-4%. Positive-pressure mechanicalventilation at a rate of 10-15 breaths/min and a tidal volume of 500 mlwas employed.

Physiologic transducers were placed as follows. 7.5 French sheathintroducers (Arrow International, Reading, Pa.) were placed in thebilateral femoral arteries. A micromanometer-tipped catheter (SPC 350,Millar Instruments, Houston, Tex.) was fed retrograde to the thoracicaorta from the femoral artery for central ABP. The catheter wasspecifically positioned to achieve a diastolic decay that appeared asexponential as possible. The second introducer was attached to stifffluid-filled tubing (Arrow International) and an external pressuretransducer (TSD104A, Biopac Systems, Santa Barbara, Calif.) for femoralABP. The chest was opened with a midline sternotomy. An ultrasonic flowprobe was placed around the aortic root for gold standard CO (T206 withA-series probes, Transonic Systems, Ithaca, N.Y.). Finally, a 23- or25-gauge angiocatheter was placed as distal as possible to the brachialartery and attached to an external pressure transducer via short, rigidtubing for “radial” ABP. Each transducer output was interfaced to amicrocomputer via an A/D conversion system (MP150WSW, Biopac Systems).The data were recorded at a sampling rate of 250 Hz and 16-bitresolution.

In each animal, a subset of the following interventions was performedover the course of 75 to 150 minutes to vary CO and other hemodynamicparameters: infusions of volume, phenylephrine, dobutamine, isuprel,esmolol, nitroglycerine, and progressive hemorrhage. Several infusionrates were implemented followed by brief recovery periods.

The technique was applied off-line to six-minute intervals (overlappingby three minutes) of the digitized “radial” and femoral ABP signals toestimate τ and proportional CO trends. The corresponding gold standardCO trends were established by averaging the aortic flow probemeasurements over the identical time intervals. Gold standard τ trendswere similarly sought by applying the technique of Bourgeois et al [4]to the central ABP signals. As a metric for comparison between anestimated trend ({circumflex over (X)}(i)) and the corresponding goldstandard trend (X₀(i)), the root-mean-square-normalized-error (RMSNE) inpercent was computed as follows:

${{RMSNE} = {{\sqrt{\frac{1}{N}{\sum\limits_{i = 1}^{N}( \frac{{\hat{X}(i)} - {X_{0}(i)}}{X_{0}(i)} )^{2}}} \cdot 100}\%}},$where N represents the number of analyzed six-minute intervals and theargument i denotes the i^(th) analyzed six-minute interval. In order touse this metric to compare an estimated proportional CO trend with thecorresponding absolute gold standard CO trend, the former trend wasfirst scaled to have the same mean value as the latter trend for eachanimal. The correlation coefficient (ρ) between the estimated and goldstandard trends was also calculated as a scale-invariant metric forcomparison.

FIG. 6 illustrates example excerpts of the digitized central, “radial”,and femoral ABP signals. The central ABP excerpt is from the beginningof the recording period in which the aortic catheter was positioned suchthat the diastolic decay appeared as exponential as possible.Unfortunately, the diastolic decay of the central ABP signal did notconsistently appear as a single exponential throughout the recordingperiod in which various interventions were employed. The “radial” andfemoral ABP excerpts are from the same time but later in the recordingperiod. Although the diastolic decay of the femoral ABP excerpt appearssmooth, it cannot be adequately represented by a single exponentialfunction.

Table 1 summarizes the results for each animal, and FIGS. 7 and 8 areexamples of the corresponding trends for animal 1 (worst result) andanimal 5 (best result). (The femoral ABP signal of animal 4 was notanalyzed due to excessive damping.) The table and figures illustrate thewide physiologic range imposed by the interventions and strong agreementbetween the estimated and gold standard CO trends (in terms of CO RMSNEand visually). This strong agreement was confirmed by high overall rvalues (mean±SD) between the gold standard CO trends and the CO trendsestimated from the “radial” (0.84±0.07) and femoral (0.86±0.05) ABPsignals. Additionally, Table 2 shows that the CO errors (differencebetween calibrated, estimated CO trends and corresponding gold standardCO trends) were largely uncorrelated with CO, mean ABP (MAP), and heartrate (HR).

TABLE 1 Summary of results. CO RANGE MAP RANGE HR RANGE CO RMSNE [%]τ_(D) RMSNE ANIMAL [L/MIN] [MMHG] [BPM] femoral “radial” [%] 1 1.6-5.229-100 96-180 19.9 19.1 8.3 2 2.3-4.2 54-127 101-204  10.2 16.0 5.9 31.9-5.8 70-120 96-186  8.8 16.7 14.7 4 1.3-4.3 27-106 103-198  — 12.3 —5 2.4-5.0 65-118 91-198 10.2 8.0 9.7 6 2.3-5.6 52-108 109-177  17.1 14.712.4 TOTAL 1.3-5.8 27-127 91-204 14.0 15.0 10.3 CO is cardiac output;MAP, mean arterial pressure; HR, heart rate; RMSNE,root-mean-square-normalized-error; and τ_(D), long time constant ofarterial tree.

TABLE 2 Correlation coefficient (ρ) matrix. ABP is arterial bloodpressure. See Table 1 caption. CO MAP HR “RADIAL” ABP CO ERRORS 0.110.47 −0.08 FEMORAL ABP CO ERRORS 0.09 0.32 0.14

Since we were not able to obtain gold standard τ_(D) trends from thecentral ABP signals, we compared the two τ_(D) trends estimated from the“radial” and femoral ABP signals, which should, in theory, beequivalent. Table 1 summarizes the comparison results in terms of τ_(D)RMSNE in which the gold standard trends were established as the averageof the two τ_(D) trend estimates. That is, the τ_(D) RMSNE here equalsthe root-mean-square of the difference between the two τ_(D) trendestimates divided by their sum and is the same for either signal. Thelow overall τ_(D) RMSNE in the table is buttressed by a high overall ρvalue (mean±SD) between the two τ_(D) trend estimates (0.85±0.08). Thus,there is solid agreement between the two τ_(D) trend estimates despitesubstantial differences in short-time scale morphology between the“radial” and femoral ABP signals (FIG. 6), and the overall COmeasurement error is only 14.6%. Preliminary studies show that thesix-minute intervals used here may be reduced to, for example,three-minute intervals without materially affecting the results.

In certain other embodiments of the invention it may be desirable toadjust the proportionality constant AC to vary depending on the arterialblood pressure or heart rate, if it is found that there is a systematicdifference between dependence of the estimated cardiac output and theabsolute cardiac output on heart rate or arterial blood pressure.

The foregoing description is to be understood as being representativeonly and is not intended to be limiting. Alternative systems andtechniques for implementing the methods of the invention will beapparent to one of skill in the art and are intended to be includedwithin the accompanying claims.

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We claim:
 1. A method for determining cardiac output to within aconstant scale factor, comprising: measuring a physiological signal of apatient using a sensor, the physiological signal indicative ofcardiovascular system activity and measured over a plurality of cardiaccycles; determining, from the physiological signal, beat-to-beatvariability of the physiological signal across multiple cardiac beats;determining cardiac output to within a constant scale factor using thebeat-to-beat variability information extracted from the physiologicalsignal; and presenting the cardiac output on a display of a computingdevice; wherein determining beat-to-beat variability includesconstructing a cardiac contractions timing signal from the physiologicalsignal by forming an impulse train in which each impulse is located atthe onset of upstroke of each pulse; determining an impulse response,which when convolved with the cardiac contractions timing signal, fitsthe physiological signal; determining a time constant by fitting anexponential function to a tail end of the impulse response; anddetermining cardiac output to within a constant scale factor using thetime constant.
 2. The method of claim 1 further comprises measuring thephysiological signal invasively or non-invasively at any site in thesystemic or pulmonary arterial tree.
 3. The method of claim 1 whereinthe physiological signal is arterial blood pressure.
 4. The method ofclaim 1 wherein the physiological signal is pulmonary arterial bloodpressure.
 5. The method of claim 1 wherein the physiological signal is asignal related to arterial blood pressure.
 6. The method of claim 1wherein determining beat-to-beat variability further comprisesestimating a function that represents the response of the physiologicalsignal to a single cardiac contraction over a time period greater than asingle cardiac cycle.
 7. The method of claim 6 further comprisesdetermining a characteristic time of the function and determiningcardiac output to within a constant scale factor by dividing themagnitude of the physiological signal by the characteristic time.
 8. Themethod of claim 1 further comprises determining vascular resistance towithin a constant scale factor using the beat-to-beat variabilityinformation.
 9. A method for determining a dynamical property of thesystemic or pulmonary arterial tree, comprising: measuring aphysiological signal of a patient using a sensor, the physiologicalsignal indicative of cardiovascular system activity over a plurality ofcardiac cycles; determining the timing of cardiac contractions inrelation to each other, which occur in a sequence of cardiaccontractions, where the determination is made from the physiologicalsignal; determining, from the timing of cardiac contractions and thephysiological signal, a mathematical relationship between the timing ofcardiac contractions in the sequence and the physiological signaloccurring over the plurality of cardiac cycles; determining a dynamicalproperty of the systemic or pulmonary arterial tree using therelationship; determining at least one of cardiac output and vascularresistance from the dynamical property; and presenting the at least oneof cardiac output and vascular resistance on a display of a computingdevice.
 10. The method of claim 9 wherein the physiological signal isarterial blood pressure.
 11. The method of claim 9 wherein thephysiological signal is a signal related to arterial blood pressure. 12.The method of claim 9 further comprises determining the timing ofcardiac contractions by measuring and analyzing a surfaceelectrocardiogram (ECG).
 13. The method of claim 9 further comprisesdetermining at least one of cardiac output and vascular resistance towithin a constant scale factor from the dynamical property.
 14. Themethod of claim 9 further comprises fitting an exponential-like functionto a portion of the relationship, estimating a time constant of thefunction and determining cardiac output to within a constant scalefactor by dividing arterial blood pressure by the time constant.
 15. Amethod for determining cardiac output to within a constant scale factor,comprising: measuring a physiological signal of a patient using asensor, the physiological signal indicative of cardiovascular systemactivity and measured over a plurality of cardiac cycles; modeling thephysiological signal as an output of a mathematical function;determining an input to the mathematical function from the physiologicalsignal, where the input is indicative of cardiac contractions;identifying the mathematical function, which when applied to the input,fits the measured physiological signal over a plurality of cardiaccycles; determining cardiac output to within a constant scale factorfrom the identified function; and presenting the cardiac output on adisplay of a computing device.
 16. The method of claim 15 furthercomprises low pass filtering the physiological signal prior to the stepof determining an input.
 17. The method of claim 15 wherein thephysiological signal is arterial blood pressure.
 18. The method of claim15 wherein the mathematical function is a convolutional equationgoverned by an impulse response.
 19. The method of claim 18 wherein theinput to the mathematical function is an impulse train or a train offinite width pulses.
 20. The method of claim 19 further comprisesidentifying the mathematical function from the input usingautoregressive exogenous input identification.
 21. The method of claim15 further comprises estimating a time constant of the mathematicalfunction and determining cardiac output to within a constant scalefactor by dividing arterial blood pressure by the time constant.